Dear @Ella,
Welcome to the Wefugees Community and thank you for reaching out to us.
I tried to give an answer on a very similar question here before. In Germany, it is not possible to simply "register" your religious marriage in order to make it official. You will need to marry at the registry office (Standesamt). For this, the civil servants most probably request your passports and other documents. You may see our blog on this topic for more details. Please note that it might be harmful for the pending asylum procedure if your partner is applying for a passport at his country of orgin's embassy in the meantime.
In any case, also don't hesitate to get back to us with any further questions.
All the best,
Meike